In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant examples are discussed. We also begin a sort of dynamical analysis of the relation, in connection with what has been recently called gamma-dynamics and gamma-symmetries, and we discuss in some details the role of different scalar products in our analysis. The case of self-adjoint operators is recovered as a special case of our general settings.

Bagarello, F. (2023). Uncertainty relation for non-Hermitian operators. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 56(42) [10.1088/1751-8121/acfbc7].

Uncertainty relation for non-Hermitian operators

Bagarello, F
2023-10-20

Abstract

In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant examples are discussed. We also begin a sort of dynamical analysis of the relation, in connection with what has been recently called gamma-dynamics and gamma-symmetries, and we discuss in some details the role of different scalar products in our analysis. The case of self-adjoint operators is recovered as a special case of our general settings.
20-ott-2023
Settore MAT/07 - Fisica Matematica
Bagarello, F. (2023). Uncertainty relation for non-Hermitian operators. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 56(42) [10.1088/1751-8121/acfbc7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/637216
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